170 CHEMICAL ENGINEERING
of this clearance on capacity can be found. For example, with a pressure ratio of p2/pi = 8, the chart shows this value for single-stage compression to be 3.3. The capacity for these conditions and a 4 per cent clearance will be 1 — (0.04 X 3.3) = 1 — 0.132, or 86.8 per cent of the piston displacement. Clearances in the larger sizes of compressors approximate 1 per cent; in smaller machines they are greater, being in some cases as high as 3 per cent.
The indicator card would be a true method of measuring the volumetric efficiency if the temperature of the air after being drawn into the cylinder were the same as that of the atmosphere, and if the pressure at the end of the suc-tion stroke were the same as that of the atmosphere. This is never the case.
The true volumetric efficiency is the ratio of the free air actually drawn in to the piston displacement.
The cylinder efficiency of an air compressor may be defined as the ratio of the work done in a complete cycle to compress isothermally a volume of air at atmospheric pressure equal to the intake piston displacement, divided by the actual work done in the air cylinder. This would be the area AKCG (Fig. 30) divided by the shaded area or -the actual work done in the air cylinder.
The efficiency of compression may be defined as the product of the cylinder efficiency and the true volumetric efficiency, or it is the work done in a complete cycle to compress isothermally (without clearance) a given volume of free air, divided by the work actually expended in compressing the same volume of free air.
The mechanical efficiency of an air compressor is the work done in the air cylinders divided by the work done in the engine cylinders if driven direct by steam or gas engine, or by the work delivered at the belt if the compressor is belt-driven.
Actual Values of Efficiencies. — Tests of piston compressors show extreme variations of mechanical efficiency from 76 to 97 per cent, with approximate averages for the more common sizes of 85 per cent. The true volumetric efficiency of piston air compressors will vary from 80 to 97 per cent, and the cylinder efficiency for water-jacketed compressors from 80 to 85 per cent. This will result in efficiencies of compression varying from 64 to 82 per cent.
Multiplying the mechanical efficiency by the efficiency of compression will show variations from 48 to 79 per cent. That is, the energy required to compress a certain amount of air isothermally is only from 48 to 79 per cent of that actually expended in the steam cylinder. Tests show that with the great majority of compressors this product ranges from 50 to 60 per cent, while with some of the best compressors under test conditions it will reach as high as 78 per cent.
Horsepower Required to Compress Air. — Disregarding clearance, the horsepower required to compress air in a single-stage compressor is :
where Vi represents the volume (cu. ft.) of free air compressed per minute and pi and pz the pressures in pound per square inch absolute.
Representing the intercooler pressure by p*t the work done in both cylinders of a two-stage compressor will be
With perfect intercooling, piVi = pt-t>,-. The above expression for the total work will be a minimum when pi = \Xpip2 as already discussed.